Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 31Citation - Scopus: 29Stability Analysis for Boundary Value Problems With Generalized Nonlocal Condition Via Hilfer-Katugampola Fractional Derivative(Springer, 2020) Kumam, Poom; Jarad, Fahd; Borisut, Piyachat; Sitthithakerngkiet, Kanokwan; Ibrahim, Alhassan; Ahmed, IdrisIn this research, we present the stability analysis of a fractional differential equation of a generalized Liouville-Caputo-type (Katugampola) via the Hilfer fractional derivative with a nonlocal integral boundary condition. Besides, we derive the relation between the proposed problem and the Volterra integral equation. Using the concepts of Banach and Krasnoselskii's fixed point theorems, we investigate the existence and uniqueness of solutions to the proposed problem. Finally, we present two examples to clarify the abstract result.Article Citation - WoS: 12Citation - Scopus: 13On a Class of Boundary Value Problems Under Abc Fractional Derivative(Springer, 2021) Jarad, Fahd; Gul, Rozi; Shah, Kamal; Khan, Zareen A.In this work, we establish some necessary results about existence theory to a class of boundary value problems (BVPs) of hybrid fractional differential equations (HFDEs) in the frame of Atangana-Baleanu-Caputo (ABC) fractional derivative. Making use of Krasnoselskii and Banach theorems, we obtain the required conditions. Some appropriate results of Hyers-Ulam (H-U) stability corresponding to the considered problem are also established. Also a pertinent example is given to demonstrate the results.Article Citation - WoS: 48Citation - Scopus: 54A Reliable and Competitive Mathematical Analysis of Ebola Epidemic Model(Springer, 2020) Ahmad, Waheed; Abbas, Mujahid; Baleanu, Dumitru; Rafiq, MuhammadThe purpose of this article is to discuss the dynamics of the spread of Ebola virus disease (EVD), a kind of fever commonly known as Ebola hemorrhagic fever. It is rare but severe and is considered to be extremely dangerous. Ebola virus transmits to people through domestic and wild animals, called transmitting agents, and then spreads into the human population through close and direct contact among individuals. To study the dynamics and to illustrate the stability pattern of Ebola virus in human population, we have developed an SEIR type model consisting of coupled nonlinear differential equations. These equations provide a good tool to discuss the mode of impact of Ebola virus on the human population through domestic and wild animals. We first formulate the proposed model and obtain the value of threshold parameter R0 for the model. We then determine both the disease-free equilibrium (DFE) and endemic equilibrium (EE) and discuss the stability of the model. We show that both the equilibrium states are locally asymptotically stable. Employing Lyapunov functions theory, global stabilities at both the levels are carried out. We use the Runge-Kutta method of order 4 (RK4) and a non-standard finite difference (NSFD) scheme for the susceptible-exposed-infected-recovered (SEIR) model. In contrast to RK4, which fails for large time step size, it is found that the NSFD scheme preserves the dynamics of the proposed model for any step size used. Numerical results along with the comparison, using different values of step size h, are provided.Article Citation - WoS: 19Citation - Scopus: 24A Coupled System of Generalized Sturm-Liouville Problems and Langevin Fractional Differential Equations in the Framework of Nonlocal and Nonsingular Derivatives(Springer, 2020) Alzabut, J.; Jonnalagadda, J. M.; Adjabi, Y.; Matar, M. M.; Baleanu, D.In this paper, we study a coupled system of generalized Sturm-Liouville problems and Langevin fractional differential equations described by Atangana-Baleanu-Caputo (ABC for short) derivatives whose formulations are based on the notable Mittag-Leffler kernel. Prior to the main results, the equivalence of the coupled system to a nonlinear system of integral equations is proved. Once that has been done, we show in detail the existence-uniqueness and Ulam stability by the aid of fixed point theorems. Further, the continuous dependence of the solutions is extensively discussed. Some examples are given to illustrate the obtained results.Article Citation - WoS: 15Citation - Scopus: 14An Algorithm for Hopf Bifurcation Analysis of a Delayed Reaction-Diffusion Model(Springer, 2017) Kayan, S.; Merdan, H.We present an algorithm for determining the existence of a Hopf bifurcation of a system of delayed reaction-diffusion equations with the Neumann boundary conditions. The conditions on parameters of the system that a Hopf bifurcation occurs as the delay parameter passes through a critical value are determined. These conditions depend on the coefficients of the characteristic equation corresponding to linearization of the system. Furthermore, an algorithm to obtain the formulas for determining the direction of the Hopf bifurcation, the stability, and period of the periodic solution is given by using the Poincare normal form and the center manifold theorem. Finally, we give several examples and some numerical simulations to show the effectiveness of the algorithm proposed.Article Citation - WoS: 25Citation - Scopus: 22Hopf Bifurcations in Lengyel-Epstein Reaction-Diffusion Model With Discrete Time Delay(Springer, 2015) Merdan, H.; Kayan, S.; Kayan,We investigate bifurcations of the Lengyel-Epstein reaction-diffusion model involving time delay under the Neumann boundary conditions. Choosing the delay parameter as a bifurcation parameter, we show that Hopf bifurcation occurs. We also determine two properties of the Hopf bifurcation, namely direction and stability, by applying the normal form theory and the center manifold reduction for partial functional differential equations.